On Tuesday, March 27, 2018 at 12:07:41 AM UTC-7, Ralf Stephan wrote: > > Hello, > I thought I'd try Sage for a casual computation. I was interested in which > numbers of the form (2^n - (-1)^n)/3 are prime. I first tried out n=23: > > sage: (2^23+1)/3 > 2796203 > sage: _.is_prime() > False > sage: factor(2796203) > 2796203 > > Just as a data point: my magma initialization file contains:
intrinsic Factorisation(n::FldRatElt) -> SeqEnum L,u:=Factorisation(Numerator(n)); L:= L cat [ <u[1],-u[2]> : u in Factorisation(Denominator(n))]; return L,u; end intrinsic; intrinsic Factorisation(n::FldFunRatMElt) -> SeqEnum L,u:=Factorisation(Numerator(n)); L:= L cat [ <u[1],-u[2]> : u in Factorisation(Denominator(n))]; return L,u; end intrinsic; intrinsic Factorisation(n::FldFunRatUElt) -> SeqEnum L,u:=Factorisation(Numerator(n)); L:= L cat [ <u[1],-u[2]> : u in Factorisation(Denominator(n))]; return L,u; end intrinsic; intrinsic Factor(a::.)->SeqEnum return Factorisation(a); end intrinsic; just because whenever I want to factor an element from a field of fractions, I am interested in the factorization of the numerator and the denominator. I'd be in favor of adapting the globals namespace factorization routine to do something similar in sage. I think sage: is_prime(12/4) False is so bad that it forces us to special-case something in the toplevel is_prime as well. I'd hope we can leave the methods as-is. It means that library-code should NOT use the top-level is_prime (but it's unlikely it does, and it's a bad idea anyway--method versions are very likely more efficient and probably more appropriate) -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
